An employer has a daily payroll of $1225 when employing some workers at $80 per day and others at $85 per day. When the number of $80 workers is increased by 5% and the number of $85 workers is decreased by 1/5, the new daily payroll is $1540. How many were originally employed at each rate?

Question

An employer has a daily payroll of $1225 when employing some workers at $80 per day and others at $85 per day. When the number of $80 workers is increased by 5% and the number of $85 workers is decreased by 1/5, the new daily payroll is $1540. How many were originally employed at each rate?

Answer 1

let the number of workers at $80 be x

let the number of workers at $85 by y

80x + 85y = 1225 ---> 16x + 17y = 245 #1

80(1.05)x + 85(.8)y = 1540
84x + 68y = 1540
21x + 17y = 385 #2

subtract #1 from #2
5x = 140
x = 28

When I then sub in x = 28 into #1
I end up with a negative y.
illogical, can't have negative number of workers.
Something is wrong with he question, or I made some silly mistake.
check over what I did, I can't find it.

Answer 2

Let's assume the original number of workers paid $80 per day is x, and the original number of workers paid $85 per day is y.

The amount paid to workers paid $80 per day is: 80x
The amount paid to workers paid $85 per day is: 85y

Given that the daily payroll is $1225, we have the first equation:
80x + 85y = 1225 ---- (Equation 1)

Now, let's calculate the new number of workers paid $80 per day and $85 per day based on the given information.

The new number of workers paid $80 per day is increased by 5%, which means it becomes: 1.05x
The new number of workers paid $85 per day is decreased by 1/5, which means it becomes: (4/5)y

The new amounts paid to workers paid $80 per day is: 80(1.05x) = 84x
The new amounts paid to workers paid $85 per day is: 85(4/5)y = 68y

Given that the new daily payroll is $1540, we have the second equation:
84x + 68y = 1540 ---- (Equation 2)

Now, we have a system of two equations:
80x + 85y = 1225 ---- (Equation 1)
84x + 68y = 1540 ---- (Equation 2)

We can solve this system of equations to find the values of x and y.

Answer 3

To solve this problem, let's first set up the equations based on the given information.

Let's say the number of workers paid at $80 per day is 'x', and the number of workers paid at $85 per day is 'y'.

According to the given information:

The daily payroll when employing some workers at $80 per day is '80x'.
The daily payroll when employing some workers at $85 per day is '85y'.
The total daily payroll is $1225, so we can write the first equation as:

80x + 85y = 1225 ---- (Equation 1)

Now, let's consider the second scenario where the number of $80 workers is increased by 5% and the number of $85 workers is decreased by 1/5.

The new number of workers paid at $80 per day is '1.05x' (increased by 5%) and the new number of workers paid at $85 per day is '0.8y' (decreased by 1/5).

The new daily payroll is $1540, so we can write the second equation as:

80(1.05x) + 85(0.8y) = 1540 ---- (Equation 2)

Now, we have a system of equations with two variables (x and y). Let's solve these equations to find the values of 'x' and 'y'.

To eliminate decimals, let's start by multiplying both sides of Equation 2 by 100:

80(1.05x) + 85(0.8y) = 1540 becomes 105x + 68y = 154000 ---- (Equation 3)

Now we have the following system of equations:

80x + 85y = 1225 ---- (Equation 1)
105x + 68y = 154000 ---- (Equation 3)

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the elimination method to solve the system:

Multiply Equation 1 by 68 and multiply Equation 3 by 85 to make the coefficients of 'y' the same:

(68 * 80x) + (68 * 85y) = (68 * 1225)
and
(105 * 80x) + (105 * 68y) = (105 * 154000)

Simplifying these equations, we get:

5440x + 5780y = 83400 ---- (Equation 4)
8400x + 5780y = 161700 ---- (Equation 5)

Now, subtract Equation 4 from Equation 5 to eliminate 'y':

(8400x + 5780y) - (5440x + 5780y) = 161700 - 83400
2960x = 78300

Divide both sides of the equation by 2960 to solve for 'x':

x = 78300 / 2960
x ≈ 26.4189

Now, substitute this value of 'x' back into Equation 1 to solve for 'y':

80(26.4189) + 85y = 1225
2113.512 + 85y = 1225
85y = 1225 - 2113.512
85y = -888.512
y ≈ -10.4489

Since the number of workers cannot be negative, it seems that there might be an error in the given information or calculations.

In order to have a valid solution, please double-check the given information or any calculations made.